Gradient of a velocity-time graph
- Acceleration is any change in the velocity of an object in a given time
- Where:
- v = final velocity (m s–1)
- u = initial velocity (m s–1)
- Δv = change in velocity (m s–1)
- Δt = change in time (s)
- As velocity is a vector quantity, this means that if the speed of an object changes, or its direction changes, then it is accelerating
- An object that slows down tends to be described as ‘decelerating’
- The gradient of a velocity-time graph is equal to the acceleration
Acceleration on a velocity-time graph
The larger the gradient, the larger the acceleration represented on a velocity-time graph
Worked example
What does the velocity-time graph look like for this acceleration-time graph?
Answer:
Step 1: Consider how velocity is represented on the acceleration-time graph
- Acceleration is the gradient of a velocity-time graph
Step 2: Consider the velocity at each section of the acceleration-time graph
- When the acceleration increases, the gradient of the velocity-time graph increases
- When acceleration reaches a maximum, this is the maximum gradient of the velocity-time graph
- When the acceleration decreases, the gradient of the velocity-time graph decreases
Examiner Tip
A summary of the areas under the graph and gradients for the different motion graphs are:
Gradient:
- The gradient of a displacement-time graph is the velocity
- The gradient of a velocity-time graph is the acceleration
Area under the graph:
- The area under a velocity-time graph is the displacement
- The area under an acceleration-time graph is the velocity